MHT CET · Maths · Area Under Curves
The area of the region bounded by \(\frac{x^2}{9}+\frac{y^2}{4}=1\) and the line \(\frac{x}{3}+\frac{y}{2}=1\) is
- A \(\frac{1}{2}(\pi-2)\) sq. units
- B \(\frac{3}{2}(\pi-2)\) sq. units
- C \(\frac{5}{4}(\pi-2)\) sq. units
- D \(\frac{2}{3}(\pi-2)\) sq. units
Answer & Solution
Correct Answer
(B) \(\frac{3}{2}(\pi-2)\) sq. units
Step-by-step Solution
Detailed explanation
Area of quarter-ellipse = \(\frac{1}{4}\pi ab = \frac{1}{4}\pi (3)(2) = \frac{3\pi}{2}\) Area of triangle formed by line and axes = \(\frac{1}{2} \times 3 \times 2 = 3\)
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